Question: Simplify the following expression: $z = \dfrac{1}{6r} + \dfrac{1}{10r}$
In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $6r$ and $10r$ $\lcm(6r, 10r) = 30r$ $ z = \dfrac{5}{5} \cdot \dfrac{1}{6r} + \dfrac{3}{3} \cdot \dfrac{1}{10r} $ $z = \dfrac{5}{30r} + \dfrac{3}{30r}$ $z = \dfrac{5 +3}{30r}$ $z = \dfrac{8}{30r}$ Simplify the expression by dividing the numerator and denominator by 2: $z = \dfrac{4}{15r}$